I offered my humble thoughts earlier. So for this I'd just like to highlight an article I found that discusses how Empires manage connectivity.

Author Jeff Vail first notes that Rome was a new type of Empire. Previous empires were largely thirst-based, but Rome became connectivity-based

Many of the major empires that preceded Rome shared a common source of formational energy. As described by historian Karl Wittfogel, they were all “hydraulic” empires. The mechanism of centralization [of the old Empires] was their shared need to pool massive labor and resources to build and maintain the irrigation works upon which their agricultural sustenance depended. Rome formed in the absence of great public-irrigation projects. As such, it required a new mechanism of political centralization to provide formational energies and counter the distributed spacing and centrifugal tendency of economic organization. Rome pioneered a new form of Empire, a connectivity empire, laying the groundwork for modern hierarchical state-economies (See Figure 4).

If we use Chirol's concept of "generations," we might call a Hydraulic Empire a "Zeroth Generation Empire" or a "Pre-Modern Empire." In a Pre-Modern, Hydraulic, of 0G Empire, the most important "flows" are the flow of labor into the center and the flow of water into the periphery. However, in a Connectivity or 1st Generation Empire the flows become much richer. Now the main flows are wealth and security, with a flow of wealth into the center and a flow of security into the periphery.

However, this is not done in a vacuum. In the Roman Empire, for example, this was done through roads.

If Rome had allows the market to function naturally, the power of the City of Rome would have gradually been reduced as other cities enjoy the economic benefits of security. A natural ebb-and-flow of exchange creates a decentralized Empire.

Visually:

However, the Romans did not want this. The Romans did not want ;the Empire' to become a decentralized polity. They wanted the Empire to remain a tool of Rome.

So the Romans purposefully warped their economy through their road network, purposefully undercutting minor hubs and linking as many nodes as possible directly to Rome.

So, some open questions

Chirol described First Generation Empires as defined by "hard power" and Second Generation Empires as defined by "soft power." But the fact that Pre-Modern Empires exported water, without which a painful death is almost immediate, shows that their power was even "harder" than Rome. So instead of "hard power" and "soft power," do we simply have a continuum of "power hardness"?

Likewise, the arteries of Pre-Modern Empires were canals that carry water, and the arteries of 1st Generation Empires were roads and ocean-routes that carried goods and men. Does this mean that the arteries of 2nd Generation Empires are telecommunication lines that carry ideas? But we know thatideasspread through the Roman road system. And many claim that information itself can be deadly. Is this another example of a continuum of power-hardness?

If America wanted to "calcify" (in Vail's words) her world power, could she arrange ultra-high-speed fiber-optic lines to all run through the continental US? Or is this form of geographic power now obsolete?

How does Rome's strategy of isolating competitive nodes harmonize with Chirol's statement that "Great empires don’t compete against other systems per se, they strive to become “the system.”"

Might there be a pattern in the phrases: Pax Romana, Pax Mongolica, Pax Britannia and Pax Americana?

That three of them were largely connected through internal waterways, high-tech roads, and/or oceans, while a fourth is a revisionist defense of a temporary barbarian occupation built-to-fail?

(compared to)

Chinggis Khan, for example, combined steppe cavalry techniques with a reorganization of the tribal structure of his forces, a not-so-healthy does of sociopathic paranoia, and, eventually, Chinese siege techniques. Despite Chirol's assertion about the Mongol imperium (which lasted, as such, for an extremely short period), it is pretty hard to know whether it was really a net positive. The Mongols did enormous damage to regions of China, destroyed the Kievan Rus', crushed the Abbasid Caliphate, and just plain killed a lot of people. The factors that led to Mongol success in warfare had very little to do with whatever contributions they brought to the world by making the east-west trade routes safer for a time.

he's clearly a genius. He also picks up this post's theme of a hydraulic Empire, if critically

I wasn't aware of Vail's work - and his book - until Dan linked to it; Vail shares some of the same sensibilities that Patrick Jackson and I have articulated in some of our collaborative pieces. That being said, the hydraulic theory of empire is, as a comprehensive account of the formation of ancient empires, probably wrong